Comparative study of multi-objective metaheuristics¶
HV quality indicator¶
| Â | NSGAII | NSGAIIDE | MOEAD | MOEADDE | SMPSO | SMSEMOA | SMSEMOADE | Friedman |
|---|---|---|---|---|---|---|---|---|
| ZCAT1 | 4.5739e-01 | 4.4856e-01 | 3.8236e-01 | 4.5528e-01 | 4.7225e-01 | 4.6443e-01 | 4.5594e-01 | + |
| ZCAT2 | 7.4821e-01 | 6.8265e-01 | 7.1347e-01 | 7.4178e-01 | 7.5774e-01 | 7.5279e-01 | 6.9481e-01 | + |
| ZCAT3 | 4.5423e-01 | 4.4184e-01 | 3.9152e-01 | 4.5397e-01 | 4.6008e-01 | 4.6266e-01 | 4.5025e-01 | + |
| ZCAT4 | 4.5787e-01 | 4.4207e-01 | 3.8360e-01 | 4.5228e-01 | 4.5377e-01 | 4.6526e-01 | 4.5420e-01 | + |
| ZCAT5 | 8.3976e-01 | 7.9271e-01 | 7.9626e-01 | 8.4084e-01 | 8.4572e-01 | 8.4525e-01 | 7.8059e-01 | + |
| ZCAT6 | 4.7590e-01 | 3.5111e-01 | 4.0893e-01 | 4.7389e-01 | 4.5857e-01 | 4.7479e-01 | 3.7197e-01 | + |
| ZCAT7 | 4.6850e-01 | 3.3128e-01 | 4.0623e-01 | 4.4802e-01 | 4.6750e-01 | 4.6846e-01 | 3.6666e-01 | + |
| ZCAT8 | 1.8032e-01 | 1.3878e-01 | 1.0475e-01 | 1.7424e-01 | 1.8370e-01 | 1.8420e-01 | 1.5374e-01 | + |
| ZCAT9 | 1.8221e-01 | 1.5072e-01 | 9.3748e-02 | 1.7621e-01 | 1.9328e-01 | 1.8579e-01 | 1.6165e-01 | + |
| ZCAT10 | 3.8785e-02 | 0.0000e+00 | 7.0956e-04 | 2.8182e-02 | 3.4216e-02 | 4.0012e-02 | 0.0000e+00 | + |
| ZCAT11 | 4.6748e-01 | 4.0678e-01 | 4.0947e-01 | 4.5408e-01 | 4.6636e-01 | 4.7310e-01 | 4.1065e-01 | + |
| ZCAT12 | 4.6409e-01 | 3.9089e-01 | 3.9663e-01 | 4.5612e-01 | 4.7046e-01 | 4.7264e-01 | 4.0000e-01 | + |
| ZCAT13 | 5.8764e-01 | 4.8620e-01 | 5.1889e-01 | 5.6819e-01 | 5.9134e-01 | 5.9074e-01 | 4.7756e-01 | + |
| ZCAT14 | 2.9580e-01 | 2.8157e-01 | 2.0431e-01 | 2.9214e-01 | 3.0711e-01 | 3.0294e-01 | 2.8382e-01 | + |
| ZCAT15 | 4.7103e-01 | 4.0621e-01 | 3.9293e-01 | 4.5679e-01 | 4.7633e-01 | 4.7473e-01 | 3.9595e-01 | + |
| ZCAT16 | 3.4716e-01 | 3.0437e-01 | 2.4772e-01 | 3.2833e-01 | 3.5259e-01 | 3.5141e-01 | 2.8733e-01 | + |
| ZCAT17 | 8.4152e-01 | 7.8311e-01 | 7.8492e-01 | 8.4281e-01 | 8.5697e-01 | 8.4525e-01 | 8.0338e-01 | + |
| ZCAT18 | 4.6617e-01 | 2.8884e-01 | 4.1328e-01 | 4.4039e-01 | 4.6751e-01 | 4.7255e-01 | 3.2445e-01 | + |
| ZCAT19 | 4.6385e-01 | 4.4182e-01 | 3.8857e-01 | 4.5455e-01 | 4.6030e-01 | 4.6873e-01 | 4.3736e-01 | + |
| ZCAT20 | 4.6348e-01 | 3.2103e-01 | 4.0914e-01 | 4.4166e-01 | 4.6504e-01 | 4.6649e-01 | 3.7100e-01 | + |
Wilcoxon rank-sum test table¶
| Â | NSGAIIDE | MOEAD | MOEADDE | SMPSO | SMSEMOA | SMSEMOADE |
|---|---|---|---|---|---|---|
| NSGAII | ++++++++++++++++++++ | ++++++++++++++++++++ | =+====+++++=++++=+++ | -====+==-=========== | -----==--=--=-==---= | =+==++++++++++++++++ |
| NSGAIIDE | +-++=--++-==-+=+=-+- | =-=----------------- | -------------------- | -------------------- | ===-===-=======+-=== | |
| MOEAD | -------------------- | -------------------- | -------------------- | -=--=++--====-=-=+-+ | ||
| MOEADDE | --==-+==-=-=--=-=-=- | -----==---------=--- | =+==+++++++++=++++++ | |||
| SMPSO | =====-==+=========== | +++=+++=++++++++++++ | ||||
| SMSEMOA | ++++++++++++++++++++ |